A Bayesian quantum state tomography along with adaptive frameworks based on linear minimum mean square error criterion

Quantum state tomography (QST) is essential for characterizing unknown quantum states. Several methods of estimating quantum states already exist and can be classified mainly into three broad classes. They are based on the criteria like maximum likelihood, linear inversion, and Bayesian framework. T...

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Bibliographic Details
Published in:New journal of physics 2023-12, Vol.25 (12), p.123001
Main Authors: Mondal, Subhadeep, Dutta, Amit Kumar
Format: Article
Language:English
Subjects:
adaptive estimation
Algorithms
Bayesian analysis
Criteria
Errors
Estimation
Hilbert space
least squares
LMMSE
Mean square errors
Methods
Physics
quantum tomography
Tomography
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Summary:Quantum state tomography (QST) is essential for characterizing unknown quantum states. Several methods of estimating quantum states already exist and can be classified mainly into three broad classes. They are based on the criteria like maximum likelihood, linear inversion, and Bayesian framework. The Bayesian framework for QST gives a better reconstruction performance. However, the existing methods of the Bayesian frameworks are computationally extensive and, most of the time require knowledge about the prior distribution of the quantum state. In this paper, we propose a Bayesian method of QST based on the linear minimum mean square error criterion, where the prior statistics are estimated and the computational complexity is comparable to that of the linear inversion based QST method. We also propose an adaptive version based on the block estimation of parameters. Extensive numerical simulations are conducted to demonstrate its efficacy over the linear inversion-based QST regarding trace distance error metric.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ad0e49